This is the production function: Y = F(K, L) = 2(L^0.5)

I am confuse to get the labour demand of L*(like the same format in Picture 1). I attached my working solution on picture 2. Is it correct?

The target is to get L* as a labour demand. Kindly help.

Thanks

b The rm's prot: H(L) = P(Y)Y WL with Y = F(L) ' FOG: H'(L) = F'(L)[P(Y) + P'(Y)Y] W = F'(L)P(Y)(1 + n5) W = 0 > The labour demand is then dened by: F'(L) ZUK with V: 1 P P 1+17Y > |n$| represents the market power of the rm: the larger 7711:, the greater the effects on the market price of a change in production